Oliver Tse: On generalized gradient flows

Abstract

The theory for variational evolutions—evolutions driven by one or more energies-or entropies—in spaces of measures has seen tremendous growth in the last decades, of which resulted in a rich framework for classical gradient systems in general metric spaces by Ambrosio, Gigli and Savaré, where the Wasserstein metric of optimal transport theory plays a fundamental role; and a theory for rate-independent systems. While these theories have allowed massive development of variational evolutions in a certain direction—gradient flows with homogeneous dissipation—physics and large-deviation theory suggest the study of generalized gradient flows—gradient flows with non-homogeneous dissipation—which are not covered in either of these established theories.
 
In this talk, I will discuss the motivation underlying the need for a generalized theory of gradient flows and how these structures can be used in practice.
 

Zoom notes: This meeting ID – 621 4469 8204 – will be the recurring meeting for the Statistics and Probability Seminar.